In Problem 6, Elmer's utility function is U(x, y) = min{x, y²}. If the price of x is $20, the price of y is $30, and Elmer chooses to consume 4 units of y, what must Elmer's income be? A) $540 B) $880 C) $440 D) $200 E) There is not enough information to tell.

Question

Quizplus · Accepted Answer

From Elmer's utility function, we know he will choose to consume 4 units of y, and x up to the point where x = y/2.
So:
x = y/2 
Thus:
U(x,y) = min{x, y} = x = y/2 
At these prices, the cost of 4 units of y is $120 (4 units * $30/unit).
Therefore, Elmer's income must be twice this amount, or $240.
Thus, the correct answer is (C) $440, which is the only option greater than $240 (Elmer's income must be at least as much as the amount he spends on consumption).

In Problem 6, Elmer's Utility Function Is U(x, Y) =